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Q & A: relative speed

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Most recent answer: 11/24/2015
Physicists routinely accelerate particles to about 99% of speed light. What if two particles travel at 99% of speed light, each in the opposite direction from the other. That would make them travel at a relative speed to each other of 1.98% of speed light, is that right?
- Iustin (age 21)
Los Angeles, CA, United States
Nope. Each particle has its own set of space-time coordinates, not the same as the person in the lab uses. According to the very well-tested equations of special relativity, each particle sees the other go by at 1.98/(1+.99*.99) c. Thatís 1.98/1.9801 or about 0.99995 c. Close but no cigar.

Mike W.

(published on 10/22/2007)

Follow-Up #1: relativistic velocities

To be thorough, your question implies that the observer IN THE LAB measures each particle's speed at 0.99c. Given that, this same observer (in the lab) sees the particles approach each other at 1.98c. The same observer also sees two opposing photons approach each other at 2.00c. The reason for emphasizing the observer IN THE LAB is that if the two particles could "see" each other (say, they were pilots of two spacecrafts) then they would not see each other approaching at 1.98c, instead they would see each other approaching (as per Mike W.) at 0.99995 c. If this is surprising, ponder the fact that the observer in spacecraft A thinks she is stationary in space -- she has no reason to think otherwise.
- Mehran (age 65)
Arlington Heights, IL

Thanks Mehran

(published on 11/24/2015)

Follow-up on this answer.